The domain of the function is f(x,y)=cos ¹(x² + y²-3) O a. {(x,y)|x>0 and y>0} O b. {(x,y)|y>0} Oc. {(x,y)| 2 ≤ x² + y² ≤ 4} Od. {(x,y)|x>0} Oe{(x,y) 1≤x² + y² ≤3}

Q: Let f(2)= z²+3z +5 (z²+9) cos(4) Find the zeros of cos(). Evaluate [ƒ(z)dz, where C : |z − 1| = 1.…

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Q: Evaluate |F. di where F = ( – 4z, F(t) = (t, sin(t), cos(t)), 0 < t < T %3D

A: Introduction: the curve C ⊂U is defined as follows for a scalar field with functionf: U Rn→ R, a…

Q: If f (x, y) = xcos (xy) then find fæ. cos (xy) – ysin (xy) O cos (y) – xysin (xy) O cos (xy) + xysin…

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Q: De min Jx when f(x, y) = cos(y – x) – x sin(y – x). 1. fr = -x sin(y – x) | 2. fa = x sin(y – x) 3.…

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Q: Find SS₂ cos (x² + y²)dA where D = {(x, y) | 4 ≤ x² + y² ≤ 36} D

A: Let's solve given double integral.

Q: Q1) Verify that the following functions u is harmonic, and find a conjugate harmonic of function…

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Q: dy ? dx If sin(x + y) = xy, what is the expression for cos(x + y) – y x – cos(x + y) (A) cos(r + y)…

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Q: För the following function f(x,y,z) = sin(3x+ y? +z²) (3 minutes) O a. f,=6xcos(3x? +y² + z²), f, =…

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Q: e. ƒ (t) = tU(t − 3) f. f(t)=sint U(t − π)

A: We have to find the Laplace transformation of the given function.

Q: Find , where : = sin (x²) cos (y) COS 6.x sin (a) cos (y) 2.x sin (a) O2.x cos (2) 2r sin (2*) cos…

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Q: Decompose the function y=(4-2x3)4 in the form y=f(u) and u=g(x)   use g(x) = 4-2x3

A: Given function      y=4-2x34  then  we have  to decompose  the given  function  in the form  y=fu…

Q: 2. If f(x, y) = x² + xy − cos(xy), find the domain and range.

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Q: Given the equation y In (x? + y² + 4) = 4, evaluate dy Assume that the equation implicitly defines y…

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Q: Find [[ cos (2² + 3²)dA where D = COS D {(x, y) | 16 ≤ x² + y² ≤ 64}

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Q: Determine a function f such that F= and calculate [Fdy, Where F(x, y, z) = sin yi+(x cos y+cos z)…

A: What is Line Integral: A line integral in mathematics is an integral in which the function to be…

Q: Given a function f(x,y,z) = (x+9) In (7y - 2) sin (2z). Find the domain of the function. a. {…

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Q: Prove that there exists a unique function f : R → R such that f (0) = 0 and f ′(x) = sin(x)

A: We have to prove that there exists a unique function satisfying given conditions.

Q: If v(1, y) is a harmonic conjugate of a harmonic function u(1,y) is also a harmonic function. show…

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Q: Given f(x, y) = cos(5x + 2y), find faz(x, y) = -25 cos (5x + 2y) fay(x, y) = -cos (5x + 2y) fyy(x,…

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Q: 8²f Let f(x, y) = cos(xe¹²) + cos(x + ey²), find əxəy O a. O b. O C. O d. -2yey² (sin(xe¹²) - x…

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Q: 53х dx (53x + 1)2 A) 3 V5x + 1 + C B) – 3 V5x + 1 + C In5 3 C) 3ln5 (V5x + 1) + C D) V5x + 1 + C 3…

A: As per the guidelines when multiple question are posted in single pic  then we are supposed to solve…

Q: The value Of (1+1)8, is equal tO O 16 4 4i

A: 1)  f(z) = (x-y)2+ 2i (x+y)Here u = (x-y)2,  v = 2(x+y)ux = 2(x-y),   uy= -2(x-y)vx = 2,  vy = 2for…

Q: = (b) ſ sin (7(x – 2y)²) dA, where T is the triangle bounded by x – 2y T 1, y = −3x and 5y = -x.

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Q: Given a function f(x,y,z) = (x+9) In (3y - 5) sin (4z). Find the domain of the function. o a. {…

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Q: Consider the function. f(x, y) = 9 - E COMITEE (b) 0 = Find D f(2, 7), where u = cos(0)i + sin(0)j.…

A: Given function:- fx,y=9-x7-y4

Q: If f(x, y)= cos(x +y), then- (+: O a. - sin (x + y) O b. - cos(x+ y) COS O c. cos(x+ y) O d. sin (x…

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Q: Evaluate sin sin(x) dx + z cos(y) dy + sin(y) dz where C is the elipse 25x² + 16y2 = 49, oriented…

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Q: g(0, 0, 0) = g(-5, 4, −3) =

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Q: (등공) of and ôf Evaluate for f (x,y) = sin (3 x- 2y) at 36

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